EDB — 18J

Exercises

1. [18J]Let \(f : (a, b)→ ℝ\) be convex. Show that, for every closed interval \(I ⊂ (a, b)\), there exists a constant \(C\) such that \(f |_ I\) is Lipschitz with constant \(C\). Provide an example of a continuous and convex function defined on a closed interval that is not Lipschitz.